X-ray study of the thermal expansion anisotropy in the quarternary semiconductor CuGaSn□Se4

Accurate lattice parameters a and c of the tetragonal chalcopyrite quaternary semiconductor CuGaSn□Se₄ have been determined as a function of temperature by the X-ray powder diffraction method in the temperature range 300 K to about 900 K. The data have been used to evaluate the axial expansion coefficients α_a and α_c at various temperatures. The thermal expansion studies revealed the anisotropy between the axial expansion coefficients having a larger coefficient of expansion along the a-axis than that along the c-axis (α_a > α_c). The mean values α_a and α_c, in the temperature range 300–900 K, are found to be 14.02 × 10^-6K^-1 and 5.02 × 10^-6K^-1 respectively, and the axial ratio, c/a, changes with a coefficient of -8.96 × 10^-6K^-1. This result indicates an increase in the tetragonal distortion, δ = 2 - c/a with temperature. An attempt is made to explain the increase in tetragonal distortion with temperature and the anisotropic thermal expansion of CuGaSn□Se₄ in terms of the thermal expansion of the A>−;Se (where A is Cu and Ga randomly distributed) and B>−;Se (where B is Sn and vacancy randomly distributed) bonds. The results are also discussed in terms of the principal Grüneisen parameters of chalcopyrite structure compounds.     

Thermal expansion of niobium diselenide in the basal plane at low temperatures

The thermal expansion of a high-quality 2H-NbSe₂ single crystal is precisely measured in the basal plane and the temperature range 5.7–50 K. An anomaly of the thermal expansion in the basal plane is detected, and it is found to be caused by a superconducting transition. The change in thermal expansion coefficient α _ab is used to calculate the pressure derivative of the critical temperature (dT _c /dp _ab ) = (19.0 ± 2.0) × 10^?9 K/Pa, and this derivative agrees well with the reported data. An additional anomaly, which indicates a phase transition, is also detected in the pretransition range. The nature of the detected phase transition is discussed.     

The thermal expansion of axial metals

The thermal expansion of axial metals is surveyed with particular reference to recent very low temperature data for zinc, cadmium, magnesium, β-tin, indium, bismuth and antimony. For a given solid, the independent thermal expansion coefficients α_⊥ and α_‖ are conveniently compared at low temperatures by plotting α_⊥/T ³ and α_‖/T ³ against T. The plots show clearly how contraction in one principal symmetry direction ensues from rapid expansion in the other direction. The Grüneisen functions γ_⊥ and γ_‖ are discussed for each solid using data from lattice-dynamical models and neutron-diffraction measurements. They show how features of the individual thermal expansions arise from a combination of vibrational, elastic and electronic effects. For these solids and for zirconium, titanium, yttrium and thallium the larger of γ_⊥ and γ_‖ at high temperatures is that referring to strains in the direction of the stronger forces (judged from the axial ratio). At lower temperatures the inequality reverses, except for tin, implying that the highest normal-mode frequencies depend most strongly on strain in the direction of the stronger forces. More experimental studies of thermal expansion at the lowest temperatures are desirable, as well as more second and third-order elastic constant data. Theoretical work is needed on realistic lattice models applicable to non-cubic metals.     

Heat capacity and lattice dynamics of yttrium diboride in the temperature range 5–300 K

This paper reports an experimental study of the heat capacity and crystal lattice parameters of a polycrystalline sample of yttrium diboride prepared by high-temperature synthesis from elements. The electronic and lattice contributions to the heat capacity are isolated. The temperature dependences of the characteristic temperature, the linear thermal expansion coefficients α_a(T) and α _c (T), the bulk thermal expansion coefficient β(T), and the Grüneisen coefficient are calculated. A region of negative values of α _c (T) and β(T) is revealed. Anharmonicity is found to exert only a minor effect on the YB₂ lattice dynamics over a larger part of the temperature range covered.     

Thermal expansion of (Sr<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>La<Subscript>x</Subscript>)<Subscript>3</Subscript>Ru<Subscript>2</Subscript>O<Subscript>7</Subscript> single crystals at low temperatures

For single-crystal samples of the (Sr_1?xLa_x)₃Ru₂O₇ ruthenates, the temperature dependence of the thermal expansion coefficient α(T)) is measured in the range 4.2–80 K. The effect of magnetic fields H ≤ 3.5 T on thermal expansion is analyzed. It is found that the (Sr_1?xLa_x)₃Ru₂O₇ ruthenates exhibit an anomalous (negative) thermal expansion coefficient in the temperature range T ≤ 18 K. The position and width of the anomaly revealed in the temperature dependence of the thermal expansion coefficient α(T)) depend substantially on the magnetic field. The origin of the thermal expansion anomaly in ruthenates, the correlation of this anomaly with the stability of the crystal lattice, and the common nature of the anomalies in the thermal properties of ruthenates and high-temperature superconductors are discussed.     

Defect formation and transport in SrFe1-xAlxO3-δ

Perovskite-related phases derived from SrFeO_3-δ are among known mixed conductors with highest oxygen permeability and are thus of interest as the ceramic membrane materials for oxygen separation and partial oxidation of light hydrocarbons. Dense ceramics of SrFe_1-xAl_xO_3-δ (x=0.1–0.5) were prepared via the glycine-nitrate process. The cubic solid solution formation was found to occur in the concentration range x=0–0.35. Increasing aluminum content leads to decreasing thermal expansion coefficients (TECs), relative fraction of Fe⁴⁺ under oxidizing conditions, and also the total conductivity, predominantly p-type electronic at oxygen pressures close to atmospheric. The TECs vary in the range (13.5–16.4)×10^?6 K^?1 at 373–923 K and increase up to (18.6–31.9)×10^?6 K^?1 at 923–1273 K. The oxygen permeation fluxes decrease moderately with aluminum additions. The Mössbauer spectroscopy data and p(O₂) dependencies of electrical properties indicate a small-polaron mechanism of electronic transport in SrFe_1-xAl_xO_3-δ. Reducing oxygen partial pressure results in transition from dominant p- to n-type electronic conduction. The low-p(O₂) stability limit of SrFe_1-xAl_xO_3-δ perovskites lies between that of LaFeO_3-δ and Fe/Fe_1-γO boundary.     

Polymorphic transformation in nanocrystalline silver sulfide

The α-Ag₂S acanthite–β-Ag₂S argentite phase transformation in nanocrystalline silver sulfide has been studied in situ for the first time using high-temperature X-ray diffraction and scanning electron microscopy. The formation of argentite has been proved by differential thermal analysis. The acanthite–argentite transformation occurs at a temperature of ～449–450 K, and its enthalpy is ～3.7–3.9 kJ mol^–1. The thermal expansion coefficients of acanthite and argentite have been estimated.     

Phase transition and anisotropy of thermal expansion in TlInS2

Linear expansion coefficients parallel and perpendicular to the layer plane of TlInS₂ layer crystal were measured in the temperature range 20–250 K at T { 200 K a strong anomaly in α⊥ behaviour was observed—the value of α6 increased abruptly up to the 200 × 10^?6 K^?1 due to phase transition in this crystal. It was shown that there is no anomaly in the behaviour of linear expansion coefficient α_z.dfnc;. This fact allowed to conclude that the phase transition in TlInS₂ is caused by changes in interlayer distances.     

Chemisorption of CO on tungsten (100): Combined flash desorption and electron stimulated desorption study. II

The chemisorption of CO on W(100) at ~ 100K has been studied using a combination of flash desorption and electron stimulated desorption (ESD) techniques. This is an extension of a similar study made for CO adsorption on W(100) at temperatures in the range 200–300K. As in the 200–300 K CO layer, both α₁-CO and α₂-CO are formed in addition to more strongly bound CO species upon adsorption at ~ 100K; the α-CO states yield CO⁺ and O⁺ respectively upon ESD. At low CO coverages, the α₁ and α₂-CO states are postulated to convert to β-CO or other strongly bound CO species upon heating. At higher CO coverages, α₁-CO converts to α₂-CO upon thermal desorption or electron stimulated desorption. There is evidence for the presence of other weakly-bound states in the low temperature CO layer having low surface concentration at saturation. The ESD behavior of the CO layer coadsorbed with hydrogen on W(100) is reported, and it is found that H(ads) suppresses either the concentration or the ionic cross section for α₁ and α₂-CO states.     

Thermal expansion of lT-TaS2 and 2H-NbSe2

The thermal expansion of the a and c axes of lT-TaS₂ and of the a axis of 2H-NbSe₂ have been measured between 4 K and 360 K. Discontinuities in the lattice parameters of TaS₂ were observed at the known charge density wave phase transitions near 200 K and 352 K, and a new transition was found near 283 K. These results are used to estimate the entropy changes occurring at the phase transitions. At the charge density wave onset temperature in NbSe₂ we find an upper limit to any discontinuity in the a axis of 2 × 10^-7 and to any discontinuity in the expansion coefficient of 3 × 10^-7 K^-1.     

Unusual thermal conductivity of the negative thermal expansion material, ZrW2O8

In order to investigate the relationship between negative thermal expansion and other thermal properties, the thermal conductivity of the α-phase of ZrW₂O₈ has been determined from 1.9 to 390 K. In addition, the heat capacity was measured from 1.9 to 300 K. The thermal conductivity of ZrW₂O₈ is low, glass-like and close to its theoretical minimum value. The phonon-phonon coupling of the highly anharmonic low-frequency modes which are responsible for negative thermal expansion in ZrW₂O₈ appears to be highly efficient, leading to short phonon mean free paths and exceptionally low thermal conductivity.     

Thermal expansion and elasticity of PdFe<Subscript>3</Subscript>N within the quasiharmonic approximation

We have explored the bulk modulus and the thermal expansion of PdFe₃N (space group Pm[`3] mPm\overline 3 m) using ab initio phonon dynamics within the quasiharmonic approximation in the temperature range from 50 to 1000 K. PdFe₃N possesses a linear thermal expansion coefficient common for typical ceramics. The calculated average linear thermal expansion coefficient of 6.4 × 10^-6 K^-1 is consistent with the average measured coefficient of 6.7 × 10^-6 K^-1. We have shown here that the thermal behavior of this compound can be understood based on the electronic structure and the lattice dynamics thereof. PdFe₃N exhibits both metallic as well as covalent-ionic bonding. The Fe–N covalent-ionic bonding suppresses the lattice vibrations of the PdFe₃ matrix. The bulk modulus of 188 GPa for PdFe₃N decreases by 15% in the temperature range studied, which is expected due to presence of stiff Fe–N bonds.     

Adsorption of nitrogen on platinum

The adsorption and desorption of nitrogen on a platinum filament have been studied by thermal desorption techniques. Nitrogen adsorption becomes significant only after any carbon contamination is removed from the surface by heating the platinum filament in oxygen, and after the CO content in the background gas is reduced substantially. At room temperature nitrogen populates an atomic tightly bound β-state, E^≠ = 19 kcal mole^?1. The saturation coverage of the (3-state is 4.5 × 10¹⁴ atoms cm^?2. Formation of the (β-state is a zero order process in the pressure range studied. At 90 K two additional α₁- and α₂-desorption peaks are observed. The activation energy for desorption for the α₂-state is 7.4 kcal mole^?1 at low coverage decreasing to 3 kcal mole^?1 at saturation of this state, 6 × 10 molecules cm^?2. The maximum total coverage in the α-states was 1.2 × 10¹⁵ molecules cm^?2. A replacement process between the β- and α-states has been observed where each atom in the (β-state excludes two molecules from the α-state.     

Thermal conductivity and expansion of PbF2 single crystals

In order to check a phenomenon of the negative correlation between ionic and thermal conductivities of solid substances, we studied the thermal conductivity and expansion of cubic PbF₂ single crystals at 50–300 and 5.6–317 K, respectively. We found that lead difluoride had a thermal expansion coefficient α that was equal to (28.5 ± 0.3)10⁻⁶ K⁻¹ at 300 K, and a thermal conductivity coefficient k(T) was equal to 1.40 ± 0.07 W/(m K) at the same temperature. Thus, the thermal conductivity for PbF₂ is the lowest among fluorite-type MF₂ (M = Ca, Sr, Ba, Cd, Pb) thermal conductivities, whereas its fluoride-ion conductivity is the highest one among MF₂ (M = Ca, Sr, Ba, Cd, Pb) ionic conductors.

     

Thermodynamic properties of the CeSn3 mixed valence compound

We have measured on the CeSn₃ compound, the expansion coefficient between 80 and 800 K at normal pressure, the isothermal compressibility in the 0–8 GPa pressure range at room temperature and the heat capacity at constant pressure in the 60–300 K temperature range. The experimental data were compared with those previously found for the isomorphous LaSn₃ phase, assumed as a proper reference material for the study of the intermediate valency states in CeSn₃. Both the thermal expansion (3α) and the isothermal compressibility (k) of CeSn₃ show behaviours quite different from those of LaSn₃: for instance, in the standard conditions, 3α is 55 × 10^?6K^?1for CeSn₃ and 38 × 10^?6K^?1for LaSn₃; k is 15 × 10^?12 Pa^?1 and 12 × 10^?12 Pa^?1 respectively for CeSn₃ and LaSn₃. The thermal behaviour of the molar specific heat at constant pressure of CeSn₃ is similar to that of LaSn₃ for temperatures lower than 50 K. In the 70–300 K temperature range, the heat capacity of CeSn₃ is clearly higher than that of LaSn₃, ΔC_p being maximum near 150 K. The analysis of the calorimetric data show that the electronic coefficient γ of CeSn₃ is temperature dependent: its value varies from 53 mJ K^?2 mole^?1 at low temperature 24 mJ K^?2 mole^?1 at 300 K.     

Thermal expansion and the heat capacity of nanocrystalline and coarse-crystalline silver sulfide Ag2S

The thermal expansion and the heat capacity of coarse-crystalline and nanocrystalline silver sulfide Ag₂S were studied by dilatometry and differential scanning calorimentry for the first time in the temperature range 290–970 K. It is found that the thermal expansion coefficient and the heat capacity of nanocrystalline silver sulfide in this temperature range are higher than those in the case of the coarse-crystalline sulfide. It is revealed that the transformation of α-Ag₂S acanthite to β-Ag₂S argentite and β-Ag₂S argentite to γ-Ag₂S phase are the first-order phase transitions; the temperatures and the enthalpies of these transformations have been determined.

     

Specific features in thermal expansion of <Emphasis Type="Italic">R</Emphasis>Fe<Subscript>11</Subscript>Ti single crystals

Thermal expansion and its anomalies in the vicinity of spin-reorientation phase transitions in single crystals of RFe₁₁Ti (R=Y, Tb, Dy, Ho, and Er) compounds are investigated by the tensometric technique in the temperature range 77–400 K. The temperature dependences of the thermal expansion coefficient α(T) are obtained. It is found that the YFe₁₁Ti and HoFe₁₁Ti uniaxial magnetic materials exhibit pronounced anomalies in the α coefficient at T=200 and 290 K. For the TbFe₁₁Ti single crystal, the α coefficient is close to zero in the vicinity of the spin-reorientation phase transition (at T=325 K). For the DyFe₁₁Ti single crystal, which is characterized by two spin-reorientation phase transitions (at T=120 and 250 K), no features in the α(T) dependence are revealed in the region of the low-temperature spin-reorientation phase transition. In the ErFe₁₁Ti single crystal, the specific feature of thermal expansion is observed at T ～ 220 K.     

Anomalous temperature dependence of elastic constant c44 in V, Nb, Ta, Pd, and Pt

The anomalous temperature dependence of elastic constant c₄₄ for elements V, Nb, Ta, Pd, and Pt, has been calculated using first-principles theory. It is shown that the variation of elastic constant for simple elements can be approximated as the sum of thermal expansion and electronic components. The thermal expansion contributes the normal linearly decreasing effect to the elastic constant with temperature, while electronic contribution is determined by the unique character of electronic structure of elements and leads to the anomalous effect to the elastic constant with temperature.     

Effect of γ irradiation on the structural and thermal properties of [N(C2H5)4]2ZnBr4 in the vicinity of a first-order phase transition

The unit cell parameters a and c of nonirradiated [N(C₂H₅)₄]₂ZnBr₄ crystals in the temperature region 90–300 K and of samples irradiated with γ rays to doses of 10⁶ and 5 × 10⁶ R in the 270-to 300-K interval were measured using x-ray diffraction. The data obtained were used to derive the thermal expansion coefficients α_a and α_c. It is shown that the parameter a increases and the parameter c decreases with increasing temperature. In the vicinity of the phase transition (PT) at T = 285 K, the temperature dependences of a(T) and c(T) reveal anomalies in the form of jumps and the α_a(T) and α_c(T) curves have a maximum and a minimum, respectively. The heat capacity of nonirradiated and irradiated [N(C₂H₅)₄]₂ZnBr₄ samples was measured by adiabatic calorimetry. A maximum was found in the C _p(T) curve at T = 285 K. Both x-ray diffraction and heat capacity measurements showed that the PT temperature decreased after γ irradiation.